A priori error analysis of the $hp$-mortar FEM for parabolic problems

TL;DR

This paper provides a detailed a priori error analysis for the $hp$-mortar finite element method applied to parabolic problems, including superconvergence results and numerical validation.

Contribution

It introduces new a priori error estimates for the $hp$-mortar FEM for parabolic problems, covering both semidiscrete and fully discrete schemes.

Findings

Error estimates in $L^2$- and $H^1$-norms for semidiscrete and fully discrete methods

Superconvergence results in negative norms under regularity assumptions

Numerical experiments confirming theoretical error bounds

Abstract

In this article we derive a priori error estimates for the $hp$-version of the mortar finite element method for parabolic initial-boundary value problems. Both semidiscrete and fully discrete methods are analysed in $L^2$- and $H^1$-norms. The superconvergence results for the solution of the semidiscrete problem are studied in an eqivalent negative norm, with an extra regularity assumption. Numerical experiments are conducted to validate the theoretical findings.